A factorial experiment was designed to test for any significant differences in the time needed to perform English to foreign language translations with two computerized language translators. Because the type of language translated was also considered a significant factor, translations were made with both systems for three different languages: Spanish, French, and German. Use the following data for translation time in hours.
| Language | |||
| Spanish | French | German | |
| System 1 | 9 | 12 | 10 |
| 13 | 16 | 14 | |
| System 2 | 5 | 18 | 15 |
| 9 | 20 | 21 | |
Test for any significant differences due to language translator system (Factor A), type of language (Factor B), and interaction. Use = .05.
a. Complete the following ANOVA table (to 2 decimals, if necessary). Round p-value to four decimal places.
| Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F | p-value |
| Factor A | |||||
| Factor B | |||||
| Interaction | |||||
| Error | |||||
| Total |
b. The p-value for Factor A is Select
less than .005
between .005 and .0125
between .0125 and .025
between .025 and .0
greater than .05
What is your conclusion with respect to Factor A?
Factor A is significant
Factor A is not significant
C. The p-value for Factor B is Select
less than .005
between .005 and .0125
between .0125 and .025
between .025 and .05
greater than .05
What is your conclusion with respect to Factor B?
Factor B is significant
Factor B is not significant
D. The p-value for the interaction of factors A and B is Select
less than .005between .005 and .0125
between .0125 and .025
between .025 and .05
greater than .05
What is your conclusion with respect to the interaction of Factors
A and B?
Select
The interaction of factors A and B is significant
The interaction of factors A and B is not significant
| Source of Variation | SS | df | MS | F | P-value |
| factor A | 16.33 | 1 | 16.33 | 1.88 | 0.2189 |
| factor B | 126.00 | 2 | 63.00 | 7.27 | 0.0249 |
| Interaction | 60.67 | 2 | 30.33 | 3.50 | 0.0983 |
| Within | 52 | 6 | 8.67 | ||
| Total | 255 | 11 |
The p-value for Factor A is greater than .05
conclusion with respect to Factor A? : Factor A is not significant
The p-value for Factor B is between .0125 and .025
conclusion with respect to Factor B? : Factor B is significant
p-value for the interaction of factors A and B is greater than .05
conclusion with respect to the interaction of Factors A and B? The interaction of factors A and B is not significant
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